How do you simplify Square root of 24 + Square root of 54?

Question

#sqrt(24)+sqrt(54)#

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Answer 1 · 2018-06-17T20:36:42

#5sqrt(6)#

As a first step you are looking for squared values that you can 'take outside' the roots. Then seeing what you can do with the remaining roots.

#24=4xx6 = 2^2xx6#
#54=2xx27=2xx3xx9=6xx3^2#

Putting this together we have:

#sqrt(24)+sqrt(56) = sqrt(2^2xx6)+sqrt(3^2xx6)#

#color(white)("dddddddddddddd") 2sqrt(6)color(white)("d")+color(white)("d")3sqrt(6)#

#color(white)("ddddddddddddddd")sqrt(6)(2+3)=5sqrt(6)#

Answer 2 · 2018-06-17T20:37:18

#sqrt(24)+sqrt(54)=color(blue)(5sqrt(6)#

#color(lime)(sqrt(24))+color(magenta)(sqrt(54))#

#color(white)("XXX")=color(lime)(sqrt(2^2 * 6))+color(magenta)(sqrt(3^2 * 6))#

#color(white)("XXX")=color(lime)(2sqrt(6)) + color(magenta)(3sqrt(6))#

#color(white)("XXX")=color(blue)(5sqrt(6))#